Question

Suppose that you just bought a​ four-year ​$1,000 coupon bond with a coupon rate of 6.5% when the market interest rate is 6.5%. One year​ later, the market interest rate falls to 4.5%.

The rate of return earned on the bond during the year was %. ​(Round your response to two decimal​ places.)

Answer 1

Current Bond price is $ 1,000 as coupon rate and market interest rate are equal.

Bond price after one year can be computed as:

Bond Price = C x [1-{1/ (1+r)ⁿ}/r ] +M/(1+r)ⁿ

Where,

M = Face Value = $1,000

C= Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

= ($1,000 x 6.5 %)/1 = $ 65

r = Rate of interest = 4.5 % or 0.045 p.a.

n = No of periods to mature = 3

Bond Price = $ 65 x [1-{1/ (1+0.045)³}/0.045 ] + $ 1,000/ (1+0.045)³

                    = $ 65 x [1-{1/ (1.045)³}/0.045 ] + $ 1,000/ 1.141166

                = $ 65 x [1-{1/ 1.141166}/0.045] + $ 1,000/ 1.141166

                = $ 65 x [(1- 0.876297)/0.045] + $ 876.2966

                = $ 65 x [0.123703/0.045] + $ 876.2966

                = $ 65 x 2.748964 + $ 876.2966

               = $ 178.6827 + $ 876.2966

               = $ 1054.979 or $ 1,054.98

Return amount = Bond value after one year – Bond price today

             = $ 1,054.98 - $ 1,000 = $ 54.98

Rate of return = $ 54.98/$ 1,000 = 0.054979 or 5.50 %